High‐accuracy two‐interval approximation for normal‐moveout function in a multi‐layered anisotropic model

Abstract

This paper discusses reducing computation costs for traveltime calculations in multi‐layered anisotropic models. Fomel and Stovas () suggested a two‐ray five‐parameter approximation that they named ‘generalized’ because it reduces to several known three‐parameter forms. Model tests, demonstrated by the authors, showed that this generalized approximation provided very high accuracy, implying it can be used in place of the exact moveout function in modelling, migration and traveltime inversion. However, detailed model studies show that for some models, with a high‐velocity layer, this approximation leads to significant errors. I develop a new three‐ray eight‐parameter approximation that provides higher accuracy and can replace the exact traveltime function that requires numerical ray calculations for each receiver. I call it a ‘two‐interval approximation’ because it uses two different equations for two offset intervals. Model tests show that this two‐interval approximation can bring much higher accuracy compared to the generalized approximation due to the use of an additional reference ray. The two‐interval new approximation can be used instead of exact traveltimes for many practical purposes.

A new parameterization for generalized moveout approximation, based on three rays

“…Shifted hyperbola approximation (Malovichko ; de Bazelaire ), rational approximation (Tsvankin and Thomsen ; Alkhalifah and Tsvankin ) and generalized moveout approximation (GMA; Fomel and Stovas ; Stovas ; Stovas and Fomel ) are more commonly employed, because of their simplicity, applicability or higher accuracy. Other known explicit moveout approximations include methods of Alkhalifah (, ), Zhang and Uren (), Taner, Treitel and Al‐Chalabi (), Ursin and Stovas (), Blias (, , ), Aleixo and Schleicher (), Ravve and Koren () and Abedi and Stovas ().…”